(x-3)(x+2)=(x-2)(x-1)

Solution for (x-3)(x+2)=(x-2)(x-1) equation:

Simplifying
(x + -3)(x + 2) = (x + -2)(x + -1)

Reorder the terms:
(-3 + x)(x + 2) = (x + -2)(x + -1)

Reorder the terms:
(-3 + x)(2 + x) = (x + -2)(x + -1)

Multiply (-3 + x) * (2 + x)
(-3(2 + x) + x(2 + x)) = (x + -2)(x + -1)
((2 * -3 + x * -3) + x(2 + x)) = (x + -2)(x + -1)
((-6 + -3x) + x(2 + x)) = (x + -2)(x + -1)
(-6 + -3x + (2 * x + x * x)) = (x + -2)(x + -1)
(-6 + -3x + (2x + x2)) = (x + -2)(x + -1)

Combine like terms: -3x + 2x = -1x
(-6 + -1x + x2) = (x + -2)(x + -1)

Reorder the terms:
-6 + -1x + x2 = (-2 + x)(x + -1)

Reorder the terms:
-6 + -1x + x2 = (-2 + x)(-1 + x)

Multiply (-2 + x) * (-1 + x)
-6 + -1x + x2 = (-2(-1 + x) + x(-1 + x))
-6 + -1x + x2 = ((-1 * -2 + x * -2) + x(-1 + x))
-6 + -1x + x2 = ((2 + -2x) + x(-1 + x))
-6 + -1x + x2 = (2 + -2x + (-1 * x + x * x))
-6 + -1x + x2 = (2 + -2x + (-1x + x2))

Combine like terms: -2x + -1x = -3x
-6 + -1x + x2 = (2 + -3x + x2)

Add '-1x2' to each side of the equation.
-6 + -1x + x2 + -1x2 = 2 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -1x + 0 = 2 + -3x + x2 + -1x2
-6 + -1x = 2 + -3x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-6 + -1x = 2 + -3x + 0
-6 + -1x = 2 + -3x

Solving
-6 + -1x = 2 + -3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3x' to each side of the equation.
-6 + -1x + 3x = 2 + -3x + 3x

Combine like terms: -1x + 3x = 2x
-6 + 2x = 2 + -3x + 3x

Combine like terms: -3x + 3x = 0
-6 + 2x = 2 + 0
-6 + 2x = 2

Add '6' to each side of the equation.
-6 + 6 + 2x = 2 + 6

Combine like terms: -6 + 6 = 0
0 + 2x = 2 + 6
2x = 2 + 6

Combine like terms: 2 + 6 = 8
2x = 8

Divide each side by '2'.
x = 4

Simplifying
x = 4